Hi
what is the voltage drop across a 9.1v Zener connected in a circuit which has a battery of 18v.
is it 8.9 i.e. (18 - 9.1) or is it 9.1v which is what the Zener suppose to maintain across its terminals all the time regardless of the source voltage?

Connecting a 9.1 volt zener directly across an 18V battery will most likely damage/destroy the zener. A zener, like a diode, is intended to be used with a current limiting resistance in series with it and the voltage source.

The voltage drop has a slight dependence on current (but much
less than a resistor or a regular diode, which is why Zener diodes are
used as voltage references) so, to get 9.1 volts (or whatever the
exact value happens to be for your unit), you need to operate
the diode at close to the recommended current. (This is the Zener
current referred to in the previous post.) In the scenario you
describe with the battery, an easy way to do this would be to put an
appropriate resistor in series with the diode.